Factors influencing Filipino children’s solutions to addition and subtraction word problems

Young Filipino children are expected to solve mathematical word problems in English, which is not their mother tongue. Because of this, it is often assumed that Filipino children have difficulties in solving problems because they cannot read or comprehend what they have read. This study tested this assumption by determining whether presenting word problems in Filipino or reading them aloud to children in either language facilitated solution accuracy. Contrary to the initial hypothesis, reading word problems aloud did not seem to improve student performance (p > 0.10). In contrast, presenting word problems in Filipino significantly improved solution accuracy (p < 0.0001) and led to differences in error patterns – children were less likely to use an inappropriate arithmetic operation when problems were presented in Filipino. However, the language of the problem had minimal effects on the more difficult Compare problem type. Finally, the benefits of using Filipino were more pronounced for low‐achieving students who may have lower proficiency in English than their high‐achieving peers (p < 0.01).     

Development of the Metacognitive Skills of Prediction and Evaluation in Children With or Without Math Disability

Metacognition refers to knowledge about one's own cognition. The present study was designed to assess metacognitive skills that either precede or follow task engagement, rather than the processes that occur during a task. Specifically, we examined prediction and evaluation skills among children with (n= 17) or without (n= 179) mathematics learning disability (MLD), from grades 2 to 4. Children were asked to predict which of several math problems they could solve correctly; later, they were asked to solve those problems. They were asked to evaluate whether their solution to each of another set of problems was correct. Children's ability to evaluate their answers to math problems improved from grade 2 to grade 3, whereas there was no change over time in the children's ability to predict which problems they could solve correctly. Children with MLD were less accurate than children without MLD in evaluating both their correct and incorrect solutions, and they were less accurate at predicting which problems they could solve correctly. However, children with MLD were as accurate as their peers in correctly predicting that they could not solve specific math problems. The findings have implications for the usefulness of children's self‐review during mathematics problem solving.     

The Performance of Chinese Primary School Students on Realistic Arithmetic Word Problems

Compared with standard arithmetic word problems demanding only the direct use of number operations and computations, realistic problems are harder to solve because children need to incorporate “real‐world” knowledge into their solutions. Using the realistic word problem testing materials developed by Verschaffel, De Corte, and Lasure [Learning and Instruction, 4(4), 273–294, 1994], two studies were designed to investigate (a) Chinese elementary school children’s ability to solve realistic word problems and (b) the different effects of two instructional interventions (warning vs. process‐oriented) on their performance. The results indicated that, contrasting to the standard problem solving, the participating children demonstrated a strong tendency to exclude real‐word knowledge and realistic considerations from their solution processes when solving the realistic problems. Process‐oriented instruction, calling for a deep‐level processing, was more likely than warning instruction to promote the activation of realistic considerations, but it was not effective at helping children arrive at realistic or correct answers. Finally, the results and their implications for mathematical teaching are discussed.     

Middle school children's strategic behavior: Classification and relation to academic achievement and mathematical problem solving

Theories of problem solving (e.g., Verschaffelet al., 2000) hold strategic behavior centralto processing mathematical word problems. Thepresent study explores 80 sixth- andseventh-grade students' self-reported use of 14categories of strategies (Zimmerman &Martinez-Pons, 1986) and the relationship ofstrategy use to academic achievement,problem-solving behaviors, and problem-solvingsuccess. High and low achievement groupsdiffered in the number of different strategiesand categories of strategies reported but notin overall number of strategies, confidence inusing strategies, or frequency of strategy use.Students whose behaviors evidenced elaborationof the word problem's text reported moreself-evaluation; organizing and transforming;and goal setting and monitoring behavior.Implications for instructional practices thatsupport active stances toward problem solvingare discussed.     

开放性数学应用问题解决的差异性研究

数学教育硕士、本科生解决开放性数学应用问题仍然是困难的,具有较高数学理论知识未必天然地能较好解决那些只用较低数学理论知识就能解答的数学应用问题;解决策略开放、结论开放、条件开放数学应用问题的难度逐渐显著增加,数学新课程重视数学应用教育促进了学生数学应用问题解决能力的发展;解决开放性数学应用问题的策略选择具有显著性差异,呈现数学思维的单一性、近迁移性等特征,误解信息、隐喻干扰等因素对被试的策略选择产生影响.     

Private speech in children with ADHD and their typically developing peers during problem-solving and inhibition tasks

This study compared private speech of children with ADHD and normal controls during problem solving and inhibition tasks. Thirty-two children (16 children with ADHD and 16 matched controls) aged 6–11 years participated. Consistent with previous studies, children with ADHD produced more task-irrelevant and task-relevant external private speech than control children during problem-solving tasks, but did not differ in their use of task-relevant internal private speech. During the inhibition/attention task (Continuous Performance Test-II), children with ADHD produced more task-relevant external and more task-relevant internal private speech, suggesting that they may have employed a less mature strategy to aid in self-regulation. The educational implications of the current study are that there should be an increased awareness of the developmental nature and functional significance of private speech and how private speech usage may differ in children with ADHD.     

Ambivalent attitudes about teaching children with attention deficit/hyperactivity disorder (ADHD)

Drawing on attitude theories from social psychology, we conducted a survey of Australian pre-service (n = 327) and in-service (n = 127) teachers’ attitudes about teaching children with attention-deficit/hyperactivity disorder (ADHD). This paper reports a content analysis of beliefs, affect and behaviours towards teaching children with ADHD and quantitative analyses pertaining to attitudinal ambivalence – that is, where a teacher may simultaneously report negative and positive evaluations of teaching children with ADHD. While on average, overall or global attitudes were mildly positive for both cohorts, considerable ambivalence about teaching children with ADHD was commonly experienced. Participants reported ambivalent beliefs, affect and behaviours, as well as ambivalence between these attitude components. Paradoxically, participants who knew more about ADHD and held stronger positive global attitudes about teaching children with ADHD reported less ambivalent behaviours towards these children, but reported more ambivalent beliefs. The implications for teachers’ professional development and training are discussed.     

Selective spatial working memory impairment in a group of children with mathematics learning disabilities and poor problem-solving skills

This study examines visual and spatial working memory skills in 35 third to fifth graders with both mathematics learning disabilities (MLD) and poor problem-solving skills and 35 of their peers with typical development (TD) on tasks involving both low and high attentional control. Results revealed that children with MLD, relative to TD children, failed spatial working memory tasks that had either low or high attentional demands but did not fail the visual tasks. In addition, children with MLD made more intrusion errors in the spatial working memory tasks requiring high attentional control than did their TD peers. Finally, as a post hoc analysis the sample of MLD was divided in two: children with severe MLD and children with low mathematical achievement. Results showed that only children with severe MLD failed in spatial working memory (WM) tasks if compared with children with low mathematical achievement and TD. The findings are discussed on the basis of their theoretical and clinical implications, in particular considering that children with MLD can benefit from spatial WM processes to solve arithmetic word problems, which involves the ability to both maintain and manipulate relevant information.     

Teaching children how to include the inversion principle in their reasoning about quantitative relations

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research on improving children’s understanding and use of the principle of inversion through interventions has only been applied to the solving of a + b − b = ? sums. The main aim of the intervention described in this article was to study the effects of teaching children about the explicit use of inversion as part of the relational calculus needed to solve inverse addition and subtraction problems using a calculator. The study showed that children taught about relational calculus differed significantly from those who were taught numerical procedures, and also that effects of the intervention were stronger when children were taught about relational calculus with mixtures of indirect and direct word problems than when these two types of problem were given to them in separate blocks.     

Reading Comprehension among College Students

The present research investigated whether an illustration and/or a warning could help students to (a) build a situational model of the problem situation and (b) solve problematic word problems (P-items) that require realistic thinking more realistically. In 2 similar studies conducted in Turkey and Belgium, the authors presented 10- to 11-year-old children with several P-items. These problems were accompanied with an illustration that depicted the problem situation and/or a warning that alerted that some items may be nonstandard. Contrary to the authors’ expectation, findings from both studies showed that neither the illustration nor the warning, or even the combination of both manipulations, had a positive impact on the number of realistic reactions.     

Visual Instruction to Enhance Teaching of Technical Subject to Design Students

Visual instruction complementing verbal lectures is known to promote learning among students. In this study, the role of visual instruction in engaging learners effectively via the simplification of technical concepts was examined. Different aspects of visualisation, such as order of presenting and dimensionality, were tested to observe their effect on students’ approach to learning and learning outcomes. In this mixed‐method quasi‐non‐experimental explanatory study, visual instruction was applied in one of the undergraduate architecture modules that teaches fundamentals of building systems, which students often find difficult to comprehend. Three key variables, including spatial cognitive ability, approach to learning and learning outcomes, were measured using statistically valid instruments along with students’ feedback and interviews. These factors were also measured for the control group that did not receive visual instruction (n = 32), to assess the effect of the intervention. When taught with visualisation, students (n = 69), showed a significant increase in deep approach to learning (e.g., deep motive: t = 2.584, p = 0.011). In interviews, students expressed a deeper interest in the subject and reported that the topic was engaging in class. Visualisation favours students with a higher spatial ability and, thus, is useful for design students who receive spatial ability training in the course. Two‐dimensional visuals must be followed and preceded by three‐dimensional visuals to provide advanced organisation and the connection of new knowledge with known organisational models to be made.     

Using Self-Generated Drawings to Solve Arithmetic Word Problems

Abstract

In this article, two intervention studies are described that were set up to investigate whether encouraging elementary students to generate drawings of arithmetic word problems facilitates problem-solving performance. The interventions consisted of 60 to 90 min of practice and showed the usefulness of self-generated drawings for solving word problems. The subjects in the first study were first and second graders, and in the second study, fifth graders. The results indicated that the fifth graders improved problem solutions after the intervention, whereas the first and second graders did not. Unlike the first and second graders, the fifth graders generated lots of drawings of word problems. The findings suggest that the nature of the difficulties children experience when solving arithmetic word problems influences their decision to generate drawings.     

Developmental Changes in Attention and Comprehension Among Children With Attention Deficit Hyperactivity Disorder

Changes in visual attention and story comprehension for children (N = 132) with attention deficit hyperactivity disorder (ADHD) and comparison peers were examined. Between the ages of 7 and 9 (Phase 1) and approximately 21 months later (Phase 2), children viewed 2 televised stories: 1 in the presence of toys and 1 in their absence. Both groups of children showed developmental increases in visual attention and stable group differences over time. Deficits in comprehension among children with ADHD, however, increased over time. Whereas comparison children’s recall of factual and causal information increased over time in both viewing conditions, children with ADHD showed no developmental improvement in recall of factual information in the toys‐present condition and no improvement in recall of causal relations in either viewing condition.     

Deaf and hard of hearing students' performance on arithmetic word problems

There has been limited research into the intersection of language and arithmetic performance of students who are deaf or hard of hearing, although previous research has shown that many of these students are delayed in both language acquisition and arithmetic performance. The researchers examined the performance on arithmetic word problems of deaf and hard of hearing students in the South-East Queensland region of Australia; they also examined these students' problem-solving strategies. It was found that performance on word problems was similar for deaf and hearing students, but that deaf students experienced delays in achieving successful performance on word problems relative to their hearing peers. The results confirm the findings of other studies showing that students who are deaf or hard of hearing experience delayed language acquisition, which affects their capacity to solve arithmetic word problems. The study conclusions stress the need for greater use of direct teaching of analytic and strategic approaches to arithmetic word problems.     

Improving expressive writing skills of children rated for ADHD symptoms

The present study examines the expressive writing abilities of children described by their teachers as having Attention Deficit Hyperactivity Disorder (ADHD) symptoms and of matched controls and the effects of two types of facilitation. A group of 35 ADHD children and matched controls are given the task of composing a letter either under standard instructions or with facilitation (a guide scheme), preceded by a brief training on how to use the facilitation. Results show that both groups drew benefit from the guide scheme. Despite the fact that differences between groups were maintained after the training for the case of spelling errors, the poorer performance of ADHD children vanished. It is concluded that ADHD children have poor expressive writing skills, but this can be improved through the help of a guide scheme preceded by brief training.     

Accuracy of primary school children’s immediate and delayed judgments of learning about problem-solving tasks

Accuracy of students’ judgments of learning (JOLs) plays an important role in self-regulated learning. Most studies on JOL accuracy have focused on learning word pairs and text but problems-solving tasks are also very important in education. This study investigated whether children in grade 3 could differentiate in their JOLs between problem-solving tasks that varied in complexity. Participants (N = 76, 8–10 years old) engaged in solving four arithmetic problems, rated mental effort invested in each problem, gave either immediate or delayed JOLs, and completed a test containing isomorphic problems. The negative correlation that was found between invested mental effort and JOLs suggested that children's JOLs are sensitive to differences in complexity of the problem-solving tasks. Results on the relative and absolute accuracy of JOLs showed that immediate JOLs were numerically higher than delayed JOLs, and relative accuracy of immediate JOLs was moderately accurate, whereas delayed JOLs were not.     

Inhibiting interference from prior knowledge: Arithmetic intrusions in algebra word problem solving

In Singapore, 6–12 year-old students are taught to solve algebra word problems with a mix of arithmetic and pre-algebraic strategies; 13–17 year-olds are typically encouraged to replace these strategies with letter-symbolic algebra. We examined whether algebra problem-solving proficiency amongst beginning learners of letter-symbolic algebra is correlated with the ability to inhibit intrusions from the earlier arithmetic strategies. Similar to typical school practice in Singapore, we asked 14 year-old students (N = 157) to use only letter-symbolic algebra to solve 9 algebra word problems. After having controlled for algebraic knowledge, working memory, and intelligence, better inhibitory ability still predicted fewer arithmetic intrusions and higher problem solving accuracy. Path analysis revealed 2 types of inhibition. Inhibition-of-reified-processes predicted accuracy through arithmetic intrusions. Inhibition-of-recently-learned-associations predicted accuracy through intelligence. Findings suggest establishing pedagogical links between arithmetic and algebraic methods may facilitate students' transition to letter-symbolic algebra.     

Group composition and its effect on female and male problem-solving in science education

Background:?Cooperative learning may help students elaborate upon problem information through interpersonal discourse, and this may provoke a higher level of thinking. Interaction stimulates students to put forward and order their thoughts, and to understand the ideas or questions of their peer learner. However, partner gender is an important variable in cooperative learning. Previous research indicates that female students profit less than male students from mixed-gender cooperative learning in physics, especially where problem-solving is involved. Female and male students have different communication styles. For example, male students tend to give their opinions and explanations directly, while females tend to avoid presenting their opinion and are more likely to initiate cooperative problem-solving by asking questions.

Purpose:?The main aim of this study was to ascertain whether partner gender influences female students' learning to solve science problems and the role female communication style plays in the cooperative learning process.

Sample:?A total of 62 high schools students (31 female, 31 male) from three schools in the Netherlands participated in the study. Students were selected from three physics classes in grade 10, with a mean age of 15.6. Students came from various family backgrounds.

Design and methods:?An experiment was carried out to test the effect of group composition on female and male students' cooperative problem-solving in science. The students were randomly assigned to dyads and three research conditions: 15 mixed-gender pairs (MG); eight female–female pairs (FF) and eight male–male pairs (MM). Students were given training in how to solve a problem as a team, and how to complete the answer sheet. All students solved the same problems in four 50-minute sessions. In each session, students were asked to solve three new and moderately structured problems working together. Each dyad had a university student as an observer. The observer's task was to log the students' time on task and to document the interactions between the students. The observers did not interfere with the communication between the students during problem-solving.

Results:?Analyses of pre- and post-test performance revealed that female students in the MG condition did not learn to solve physics problems as well as male partners or as female students in all-female dyads. Analyses of interactive behaviours showed that female students in the MG condition devoted less time to actively seeking solutions and spent more time asking questions than their male partners.

Conclusions:?Difference in solution-seeking behaviour could explain an important part of the difference in problem-solving performance between the female and male students in this study. Female students in the all-female dyads did not differ in interactive behaviour or post-test performance from males. They had a more balanced interactive style than females in the mixed-gender dyads. Suggestions for further research are discussed. It would be interesting to examine if the findings of this study carried over to areas in which females are traditionally more comfortable, such as biology.     

The role of the working memory and language skills in the prediction of word problem solving in 4- to 7-year-old children

The aim of this study was to analyse the role of verbal and visuo-spatial working memory (WM) and language skills (vocabulary, listening comprehension) in predicting preschool and kindergarten-aged children’s ability to solve mathematical word problems presented orally. The participants were 116 Finnish-speaking children aged 4–7?years. The results showed that verbal WM (VWM) did not have a direct effect on word problems in young children but was indirectly related to word problems through vocabulary and listening comprehension. These results suggest that in young children, VWM resources support language skills which, furthermore, contribute to variation in solving orally presented word problems. The results also showed that visuo-spatial WM had a direct effect on performance in word problems, suggesting that it plays an important role in word problem solving among this age group.     

The acquisition of problem-solving skills in mathematics: How animations can aid understanding of structural problem features and solution procedures

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations would be most effective for acquiring these prerequisites, because they show the continuous transition from a concrete, but superficial problem representation to a more abstract, mathematical problem model that forms a basis for solving a problem. An experiment was conducted, where N = 32 pupils from a German high school studied either only text-based worked examples explaining different problem categories from the domain of algebra or worked examples augmented with hybrid animations. Learners with hybrid animations showed superior problem-solving performance for problems of different transfer distance relative to those in the text-only condition.